Do I accept that my brother agreed to call me each week from Florida as support for me although he admitted he doesn’t want to?

Be leary. He may have diabolical motives. My brother told me to vent all I wanted with him & when I did I think he told mom. I thought I could trust him.
If he is the "golden child" in your parent's eyes then beware.
I would not have you used like I am.
I hope this is not the case with you.

Do we have the same brother? Sounds like he is "checking out" of the situation and hopes that what he doesn't know won't hurt him.
Many of us are going it alone - without help from sibs and other family. Sorry that he doesn't seem to want to participate in your Mom's care.
Do yourself a favor and hire a paid caregiver to look in on your Mom while you take your family on a nice vacation. Look at it this way, if you become incapacitated, who will take care of your Mother?

Give the phone to your parent when he calls, and go take a nap or give yourself a pedicure. Long distance siblings haven't a clue how hard your life is but they have a responsibility to support in whatever way possible. Let him do this grudgingly or not.